In a 5-quart pot boil about 3-4 quarts of water over high heat. Slice a shallow “X” on top of each tomato. Working in batches, drop the tomatoes in the hot water for 1 minute or so. Using a slotted spoon, lift the tomatoes out and place them on a cutting board. Let tomatoes cool and then peel off the skins using your hands. Discard the water from the pot.
Roughly chop the tomatoes, core, and transfer them to the same 5-quart pot.
Peel the apples, remove cores and roughly chop. Place them in the pot with tomatoes. Add in salt, black pepper, ground coriander, Italian seasonings, paprika, garlic powder, onion powder, ground cinnamon, ground cloves, and ground nutmeg. Stir well.
Bring the mixture to a simmer over medium heat. Continue simmering, stirring occasionally, until most of the liquid is reduced and the sauce reaches the consistency you like. This will take about 2 - 3 hours but could take longer if there's a lot of liquid in the ketchup mixture.
Remove from heat and let it cool slightly. Then using a hand blender, food processor, or countertop blender blend the ketchup mixture into a smooth puree.
Strain the mixture through a fine-mesh strainer using a spoon or spatula to press the mixture through the strainer into a clean large bowl. Discard anything leftover in the strainer.
Return the ketchup back to the pot and add the vinegar. Stir well and simmer again, stirring carefully for 2-3 minutes. Taste and adjust seasonings as desired.